Suppose X is a random variable with discrete probability mass function f(x;p), where p is an unknown parameter, and possible values of X is {0,1,2,3,4,5}. Consider a hull hypothesis, H0: p=0.5 and alt. hypothesis H1: p=0.6. The probability distribution under H0 and H1 are given as follows (denoting f(x) as f(x;p)). Under H0: f(0)= 0.02, f(1)=0.03, f(2)=0.05, f(3)=0.05 f(4)=0.35, f(5)=0.50. Under H1: f(0)= 0.04, f(1)=0.05, f(2)=0.08, f(3)=0.12 f(4)=0.41, f(5)=0.30. Suppose size of the type-I error is 0.05 for a test with critical region {0,1} (with sample size 1). Then the type-II error and the power of the test, respectively, are ????
Answers
A={x:x∈N,x is a factor of 6}={1,2,3,6}.
and B={x,x∈N,xis a factor of 8}={1,2,4,8}
(i) A∪B={1,2,3,6}∪{1,2,3,6}∪{1,2,4,8}={1,2,4,8}.
(ii)A∪B={1,2,3,6}∩{1,2,4,8}={1,2}.
(iii)A−B={1,2,3,6}−{1,2,4,8}={3,6}.
(iv)B−A={1,2,4,8}−{1,2,3,6}=
Answer:
Suppose X is a random variable with discrete probability mass function f(x;p), where p is an unknown parameter, and possible values of X is {0,1,2,3,4,5}. Consider a hull hypothesis, H0: p=0.5 and alt. hypothesis H1: p=0.6. The probability distribution under H0 and H1 are given as follows (denoting f(x) as f(x;p)). Under H0: f(0)= 0.02, f(1)=0.03, f(2)=0.05, f(3)=0.05 f(4)=0.35, f(5)=0.50. Under H1: f(0)= 0.04, f(1)=0.05, f(2)=0.08, f(3)=0.12 f(4)=0.41, f(5)=0.30. Suppose size of the type-I error is 0.05 for a test with critical region {0,1} (with sample size 1). Then the type-II error and the power of the test, respectively, are ????
sorry for spam..!